pierre force 12 Pascal and philosophical method The idea of a philosophical method is more commonly associated with Descartes than it is with Pascal. In his Discourse on the Method for Conducting One’s Reason Well and for Seeking Truth in the Sci- ences, first published in 1637, Descartes asserts that, in order to be successful, the search for philosophical and scientific truths has to obey a fixed set of guidelines. In contrast, Pascal generally uses the term method ironically and pejoratively. In the Provincial Letters the various techniques used by the Jesuits to twist the precepts of conventional morality are often referred to as a method.1 In the Pensees´ , the word method is almost entirely absent. There exists one work, however, where Pascal uses the term in a non-pejorative way: a small, unfinished treatise written around 1655 and entitled Mathe- matical Mind (De l’esprit geom´ etrique´ ). In a bold claim reminiscent of Descartes’ Discourse on Method, Pascal presents the treatise as ‘the method for mathematical [i.e., methodical and perfect] demon- strations’ (OC ii, 155). More generally, he presents mathematical reasoning as the model that one should emulate in every intellec- tual activity. A study of Pascal’s philosophical method must thus begin with an analysis of Mathematical Mind. the example of mathematics The method presented in Mathematical Mind is not aimed at dis- covering scientific or philosophical truths. According to Pascal, there are ‘three principal objects in the study of truth: first, to discover it when one is searching for it; second, to demonstrate it when one possesses it; third, to distinguish it from untruth when one exam- ines it’ (OC ii, 154). Pascal goes on to say that his treatise does not 216 Cambridge Companions Online © Cambridge University Press, 2006 Pascal and philosophical method 217 address the first object (the art of finding truths that were previously unknown) because the issue has been addressed extensively and ex- cellently by others (a probable allusion to Descartes’ Discourse on Method, or to the work of Franc¸ois Viete,` who developed rules for the discovery of truths through analysis). The treatise addresses the second object (how to demonstrate truth when one possesses it) and the third by implication (because the rules one uses for demonstrat- ing true propositions can also be applied to distinguish them from false ones). In short, the purpose of the treatise is ‘to demonstrate those truths that are already known, and to shed light on them in such a way that they will be proven irrefutably’ (OC ii, 154). The beginning of the treatise contains some sweeping claims. Pascal argues that mathematics provides the one and only method for conducting perfect demonstrations: ‘Only this science’, he says, ‘possesses the true rules of reasoning’, because ‘it is based on the true method for conducting one’s reason in all things’. Pascal adds that mathematics teaches this method only by example, and that ‘it produces no discourse about it’ (OC ii, 154). In other words, math- ematicians practise the perfect method for demonstrations, but no mathematician has ever stated what the rules of this method are. As a result, this method is ‘unknown to almost everyone’ (OC ii, 155). The purpose of the treatise is, therefore, to explicate these rules in order to make them applicable beyond mathematics to the entire uni- verse of intellectual activity. Whoever possesses this method, Pascal claims, will have an edge over his interlocutors, ‘because we can see that in contests between minds that are equally strong in all other respects, the mathematical one wins’ (OC ii, 155). For Pascal, mathematics is the only human science capable of producing flawless demonstrations, ‘because it is the only one to follow the true method’, while all other sciences, ‘due to their very nature have some degree of confusion’ (OC ii, 155). Before sharing the rules of the true method with his reader, Pascal embarks on a digression. He mentions another method that is ‘even loftier and more accomplished’ (OC ii, 155) than the method of mathematics. It is, however, out of reach for human beings, ‘because what is beyond mathematics is beyond us’ (OC ii, 155). This most excellent method comprises only two rules. First, one must define every term (give a clear explanation of every term used in the demonstration). Second, one must prove every proposition (in other words, back up every Cambridge Companions Online © Cambridge University Press, 2006 218 pierre force single proposition with truths that are already known). According to Pascal, ‘this would be a truly beautiful method, but it is an entirely impossible one’ (OC ii, 157), because the need to define all terms would lead to infinite regress. As always in Pascal, the digression is a way of driving home an essential point: in order to ascertain what the perfect method is, let us assume what it would be in theory. In theory, one should define everything and prove everything, but anyone who tries to implement this method will keep defining terms ad infinitum. Pascal’s point is that the problem does not lie with the method itself; it lies with the limitations of the human mind. The fact that the perfect method leads to infinite regress proves that ‘men are naturally and permanently unable to practise any science whatsoever in an absolutely perfect order’ (OC ii, 157). Nevertheless, this does not mean that no order whatsoever is pos- sible. The order of mathematics is available. For Pascal, the virtue of mathematics is that it is perfectly suited to both the strengths and the limitations of the human mind: This order, the most perfect among men, does not consist in defining or demonstrating everything, nor does it consist in defining or demonstrating nothing; rather it holds the middle ground: it does not define those things that are clear and well understood by all men, and it defines everything else; it does not prove those things that are known to all men, and it proves everything else. (OC ii, 157) The method of mathematics is exemplary because it occupies the middle ground between a more perfect method that is beyond the reach of the human mind, and an absence of method that underes- timates our intellectual capacities. One must add that, for Pascal, the order of mathematics is inferior to the more perfect method de- scribed above ‘only because it is less persuasive, not because it is less certain’ (OC ii, 157). Pascal makes it clear from the beginning of Mathematical Mind that he does not concern himself with the method for discovering truths that are previously unknown. In this treatise, certainty is a given. The focus is on persuasion. knowledge of first principles In the practice of mathematics, what saves us from infinite regress is the fact that we arrive at ‘primitive terms that can no longer be defined, as well as principles so clear that no clearer principles are Cambridge Companions Online © Cambridge University Press, 2006 Pascal and philosophical method 219 available to prove them’ (OC ii, 157). Mathematicians do not de- fine such primitive terms as space, number, movement or equality. Similarly, says Pascal, physicists should not try to define terms such as time, and philosophers would be well advised to abstain from defining man and being. Attempting to define such terms, which are perfectly clear and understandable to all, would only bring more confusion. In that sense, the true method consists in avoiding two opposite errors: trying to define everything, and neglecting to define those things that are not self-evident. One might be surprised that mathematics is incapable of defining its principal objects of study (number, movement, space), but, Pascal argues, ‘the lack of definition is a perfection rather than a shortcom- ing; it comes not from obscurity but from complete self-evidence’ (OC ii, 162). This self-evidence is such that, ‘even though it lacks the persuasiveness of demonstration, it has the exact same degree of certainty as demonstration’ (OC ii, 162). A primitive term cannot be defined because nothing clearer than the term itself is available to explain it. In that sense, primitive terms and first principles are ‘clear and certain by the light of nature’(OC ii, 157). The order of mathematics is, therefore, ‘perfectly true, supported as it is by nature rather than discourse’ (OC ii, 157). Pascal’s reflection on the relationship between demonstration and first principles is in many ways consistent with the Aristotelian tradition. In the Posterior Analytics Aristotle argues that ‘not all knowledge is demonstrative’ and that ‘the knowledge of first princi- ples is not by demonstration’, because ‘it is necessary to know the principles from which the demonstration proceeds, and if the regress ends with the first principles, the latter must be indemonstrable’.2 Aristotle draws a clear distinction between scientific knowledge and the knowledge of first principles. Scientific knowledge is the province of discursive reasoning. The first principles, however, ‘must be apprehended by Intuition’.3 For Aristotle, wisdom is a combi- nation of discursive reasoning and intuition: ‘The wise man there- fore must not only know the conclusions that follow from his first principles, but also have a true conception of those principles them- selves. Hence Wisdom must be a combination of Intuition [nous] and Scientific Knowledge [episteme]’.4 Pascal does not appropriate the Aristotelian tradition without sub- mitting it to a major reinterpretation. In Aristotle, it is implied that not all minds have a sound intuition of first principles, because these Cambridge Companions Online © Cambridge University Press, 2006 220 pierre force principles must be reached by laborious induction: ‘Induction sup- plies a first principle or universal, deduction works from univer- sals; therefore there are first principles from which deduction starts, which cannot be proven by deduction [syllogismos]; therefore they are reached by induction [epagoge].’5 In Pascal, on the other hand, the knowledge of first principles is given by nature and is readily avail- able to all.